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The cubic Laves phase compound CeRu2 with a Kagome substructure of Ru has been investigated to understand myriad fascinating phenomena resulting from competition among its various physical and geometric features. Such phenomena include flat bands, van Hove singularities, Dirac cones, reentrant superconductivity, magnetism, the Fulde–Ferrell–Larkin–Ovchinnikov state, valence fluctuations, time-irreversible anisotropic s-state superconductivity, etc. Extensive studies have thus been carried out since 1958 when the highly unusual coexistence of superconductivity and ferromagnetism was proposed for the mixed compounds (Ce,Gd)Ru2. Activity has accelerated in recent years due to increasing interest in topological states in superconductors. However, there has been little investigation of the mutual influence of these fascinating states. Therefore, we systematically investigated the superconductivity and possible Fermi surface topological change in CeRu2 via magnetic, resistivity, and structural measurements under pressure up to ~168 GPa. An unusual phase diagram that suggests an intriguing interplay between the compound’s superconducting order and Fermi surface topological order has been constructed. A resurgence in its superconducting transition temperature was observed above 28 GPa. Our experiments have identified a structural transition above 76 GPa and a few tantalizing phase transitions driven by high pressure. Our high-pressure results further suggest that superconductivity and Fermi surface topology in CeRu2 are strongly intertwined,